[Paper Review] Multivariate Realized Volatility Forecasting with Graph Neural Network

Qinkai Chen, Christian-Yann Robert|arXiv (Cornell University)|Dec 16, 2021

Energy Load and Power Forecasting4 citations

TL;DR

This paper proposes Graph Transformer Network for Volatility Forecasting (GTN-VF), a multivariate model that integrates limit order book features with cross-sectional and temporal relationships from multiple sources using graph neural networks. Evaluated on ~500 S&P 500 stocks, GTN-VF significantly outperforms univariate and multivariate benchmarks in forecasting short-term realized volatility across different horizons.

ABSTRACT

The existing publications demonstrate that the limit order book data is useful in predicting short-term volatility in stock markets. Since stocks are not independent, changes on one stock can also impact other related stocks. In this paper, we are interested in forecasting short-term realized volatility in a multivariate approach based on limit order book data and relational data. To achieve this goal, we introduce Graph Transformer Network for Volatility Forecasting. The model allows to combine limit order book features and an unlimited number of temporal and cross-sectional relations from different sources. Through experiments based on about 500 stocks from S&P 500 index, we find a better performance for our model than for other benchmarks.

Motivation & Objective

• To improve short-term realized volatility forecasting by modeling interdependencies among stocks beyond univariate approaches.
• To integrate diverse relational data—temporal and cross-sectional—into a unified volatility forecasting framework.
• To develop a scalable graph-based deep learning model capable of handling an unlimited number of relational sources.
• To evaluate the effectiveness of different relational granularities (e.g., GICS sectors) in enhancing prediction accuracy.
• To assess model performance across varying stock liquidity levels and node connectivity.

Proposed method

• The model uses a Graph Transformer Network (GTN-VF) that processes limit order book features and relational data from multiple sources as a dynamic graph.
• Nodes represent individual stocks, and edges are constructed from multiple relational sources: GICS sector hierarchy, feature correlation, and co-movement patterns.
• The graph structure supports an unlimited number of relations, enabling flexible integration of temporal and cross-sectional dependencies.
• Message passing mechanisms in the GNN allow each node to aggregate information from its neighbors, capturing systemic risk spillovers.
• The model employs a Transformer-based architecture to capture long-range dependencies in both time and relational structure.
• Training is performed using a multi-head attention mechanism over graph-structured data, with loss minimized via RMSPE on realized volatility predictions.

Experimental results

Research questions

• RQ1 Can a graph neural network effectively combine limit order book data and multiple relational sources to improve multivariate realized volatility forecasting?
• RQ2 How does the inclusion of cross-sectional and temporal relationships affect forecasting accuracy compared to univariate models?
• RQ3 What is the optimal granularity of sector-based relationships (e.g., Industry vs. SubIndustry) for volatility prediction?
• RQ4 Does the model’s performance vary meaningfully across stocks of different liquidity levels?
• RQ5 How does node connectivity influence prediction accuracy, and does the model benefit more from connected nodes?

Key findings

• GTN-VF significantly outperforms both univariate and multivariate benchmarks in forecasting realized volatility across all tested horizons.
• The model achieves a 2% improvement in RMSPE on the most liquid stocks and up to 8% improvement on the least liquid stocks compared to a naive baseline.
• Using Industry-level GICS sector relationships yields the best trade-off between performance and computational feasibility, with test RMSPE of 0.2422.
• Adding more edges (e.g., IndustryGroup or SubIndustry) slightly reduces performance, indicating that relation quality matters more than quantity.
• Nodes with higher connectivity show consistently lower RMSPE, confirming that information aggregation from neighbors enhances prediction accuracy.
• Longer forecasting and observation windows improve performance, as volatility jumps are more detectable over extended horizons.